In this paper, a dynamic analysis on the balancing of the fluctuating input torque in a planar multi-link conveying machine is carried out, as a practical example of an automatic conveying machine which generates an L-path. Namely a planar 12-link conveying machine is proposed, which is made by joining a slider-crank mechanism to the input link of the 9-link mechanism, for the purpose of neglecting the influences of the inertia force in the links. Moreover, optimum distributed masses and moments of inertia of the plural oscillating links are determined so as to reduce the fluctuation of the torque affecting input link. Based on the above analytical results, the dynamic characteristics of the machine are investigated theoretically and experimentally. As a result, it has been obvious that the maximum magnitudes of the torque affecting the input link reduce up to approximately one third the level of that which was measured at a state of unbalance. At the same time, the positioning accuracy of the machine hand at the edge points of the path can be greatly improved.